The charged offense is "falsifying business records," Penal Law § 175.05, "of an enterprise," Penal Law § 175.05(1). The relevant definitions, contained in Penal Law 175.00, are broad:
There may be relevant caselaw, but I'm not in a position to research it.1. "Enterprise" means any entity of one or more persons, corporate or otherwise, public or private, engaged in business, commercial, professional, industrial, eleemosynary, social, political or governmental activity.
2. "Business record" means any writing or article, including computer data or a computer program, kept or maintained by an enterprise for the purpose of evidencing or reflecting its condition or activity.
Sure, a skillful lawyer might be able to plant seeds of doubt by focusing on the word "personal," but it could be an uphill battle against the charge. I don't presently think that this represents the prosecution's most challenging vulnerability.
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* It's not clear to me what "the truth of the matter asserted" means in the context of a check, apart from a statement in the memo field along the lines of "we sure pulled the wool over the election officials with the scheme carried out with this check." But so far as I know, there aren't any such a statements. Also, too, there is caselaw (although I haven't looked at it for decades) to the effect that carefully maintained personal checking account records can be admitted as the records of a regularly conducted activity, even when it's not "business activity." And I can't recall encountering any particular difficulty in getting checks admitted.
Edit: fixed citation to § 175.05(1)